401-4116-12L  Lectures on Drinfeld Modules

SemesterSpring Semester 2021
LecturersR. Pink
Periodicitynon-recurring course
Language of instructionEnglish



Courses

NumberTitleHoursLecturers
401-4116-12 VLectures on Drinfeld Modules
Starts Tuesdays and Wednesdays at 16:15.
3 hrs
Tue/2w16:00-18:00ON LI NE »
Wed16:00-18:00ON LI NE »
R. Pink

Catalogue data

AbstractDrinfeld modules: Basic theory, analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations, endomorphism rings, etc.
Objective
ContentA central role in the arithmetic of fields of positive characteristic p is played by the Frobenius map x ---> x^p. The theory of Drinfeld modules exploits this map in a systematic fashion. Drinfeld modules of rank 1 can be viewed as analogues of the multiplicative group and are used in the class field theory of global function fields. Drinfeld modules of arbitrary rank possess a rich theory which has many aspects in common with that of elliptic curves, including analytic uniformization, moduli spaces, good/bad/semistable reduction, Tate modules, Galois representations.

A full understanding of Drinfeld modules requires some knowledge in the arithmetic of function fields and, for comparison, the arithmetic of elliptic curves, which cannot all be presented in the framework of this course. Relevant results from these areas will be presented only cursorily when they are needed, but a fair amount of the theory can be developed without them.
LiteratureDrinfeld, V. G.: Elliptic modules (Russian), Mat. Sbornik 94 (1974), 594--627, translated in Math. USSR Sbornik 23 (1974), 561--592.

Deligne, P., Husemöller, D: Survey of Drinfeld modules, Contemp. Math. 67, 1987, 25-91.

Goss, D.: Basic structures in function field arithmetic. Springer-Verlag, 1996.

Drinfeld modules, modular schemes and applications. Proceedings of the workshop held in Alden-Biesen, September 9¿14, 1996. Edited by E.-U. Gekeler, M. van der Put, M. Reversat and J. Van Geel. World Scientific Publishing Co., Inc., River Edge, NJ, 1997.

Thakur, Dinesh S.: Function field arithmetic. World Scientific Publishing Co., Inc., River Edge, NJ, 2004.

Further literature will be indicated during the course

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersR. Pink
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationoral 20 minutes
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

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Offered in

ProgrammeSectionType
Doctoral Department of MathematicsGraduate SchoolWInformation
Mathematics BachelorSelection: Algebra, Number Thy, Topology, Discrete Mathematics, LogicWInformation
Mathematics MasterSelection: Algebra, Number Thy, Topology, Discrete Mathematics, LogicWInformation